Final answer:
The slope-intercept form of the equation of the line perpendicular to y = -2x - 1 through (-5, -1) is y = 1/2(x + 5) - 1.
Step-by-step explanation:
To find the equation of a line perpendicular to a given line, we need to find its slope. The given line has a slope of -2. Since perpendicular lines have slopes that are negative reciprocals of each other, the slope of the perpendicular line is 1/2.
Using the point-slope form of the equation, y - y1 = m(x - x1), where (x1, y1) is a point on the line, we can plug in the coordinates (-5, -1) and the slope of 1/2 to get:
y - (-1) = 1/2(x - (-5))
Simplifying, we get y + 1 = 1/2(x + 5).
Further simplifying, we end up with the slope-intercept form of the equation:
y = 1/2(x + 5) - 1